Random quantum circuits are used as a toy model to describe a vast variety of physical phenomena. The most important property of random quantum circuits is the ability to approximate random unitary operators and random quantum states. The latter are used in a vast range of physical fields due to their entanglement properties. The main concern will be how to optimize a family of random quantum circuits, so that we can obtain maximal entanglement with the help of the smallest possible number of quantum gates. Optimal random quantum gates can be used to physically implement a quantum circuit or as a better approximation of random quantum processes.
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